If that were true, there would be other indications, other devices, even partials or remnants. Perhaps we just do not correctly perceive what we do know of, such as catapults.

It is also quite likely that this device was the singular work of one person. Its construction does not necessitate the prior existence of machine tools, except, of course, iron hand tools for cutting bronze.

The Antikythera Mechanism is fascinating, both the story and the thing itself.
It required no technology that was not available at that time - as far as we can tell.
It was made with human inventiveness of the highest order in that good workmanship and current materials could be used to do something that was a completely new idea, to enable prediction of positions and movements of the planets as seen from a position on earth.

Read the article. Follow the story. The device was found amid other treasures in a wreck on the floor of the Mediterranean. Some of the bronze statues were the finest known since. One easy explanation is that the Antikythera Device was among the loot from Greek cities being taken to Rome.

The reason that so many classical statues have no noses is that they were defaced when mobs of Christians ran through the streets smashing idols.

We easily cite the Caliph Omar and the general Amir ibn al-As who destroyed the Library at Alexandria. "If the books agree with the Quran they are unnecessary. If they disagree, they are heresy." But Paul said, "Beware that any man destroy you through philosophy."

On the other hand, we know of the great library at Baghdad and, of course, those hard-working scribes of the European Dark Ages. Similarly, various mechanical devices were used and improved upon.

Specifically preserving knowledge is especially important.

I also expect civilization to continue to expand and extend. I agree that the world of 2112 may be less recognizable to us than our world would be to a Roman.

And of all the things lost with the fall of Rome, the worst was not the Etruscan language. People still speak ancient languages such as Basque and Lithuanian. The Etruscans just died out, culturally. (They are still with us: we call them "Florentines" from "Tuscany.") I think that the fall of Rome was hallmarked by the loss of cement. Portland cement had to be reinvented.

As I point out in this blog post
http://necessaryfacts.blogspot.com/20...
Latin was still a preferred language for scholars into the 19th century. Even in the high Middle Ages, as vernaculars were rising, the reason that there is something called "Medieval Latin" is that more-or-less ordinary people across Europe still used the language, but gave it new style. They no longer wrote like Cicero, and they knew it.

Something lost, something gained...

I think that the worse catastrophe was the Bronze Age Collapse. (Perhaps geological: Moses at the Red Sea; the Minoan fleet swept from the Mediterranean; city walls crumbled and cities exposed.) But, there, too, we have arguable evidence. And however slowly civilization recovered.

As for Foundation, just a quick note. You may be right that some planet was burning coal, but mostly, it was just the recession of the Empire and the rise of local rule. They still had space travel - even hyperspace, apparently - and all the rest. But the collapse was clear. And it was deep. Hari Seldon sold the emperor on the establishment of Terminus to preserve the knowledge of the Empire with the Encyclopedia Galactica. The very fact that the emperor accepted preservation was an example of the loss of spirit, of a loss of "psychic" or cultural "energy" across the galaxy. We see a lot of that here in the Gulch.

Asimov wrote:
"So success is not a mystery, just brush up on your history, and borrow day by day.
Take an Empire that was Roman and you'll find it is at home in all the starry Milky Way.
With a drive that's hyperspatial, through the parsecs you will race, you'll find that plotting is a breeze,
With a tiny bit of cribbin' from the works of Edward Gibbon and that Greek, Thucydides."

(More on Foundation in a different topic.)

Archimedes was a brilliant mathematician for the intellectual state of the age he worked in, but he did not come close to inventing calculus. His method of exhaustion was repeated and verified over and over for each calculation of certain type, and he did not generalize and have the concepts of calculus, including limits, only the beginning of the idea of the method underlying it. His method of exhaustion, was a great accomplishment, but was the beginning of a long progression of development (picked up again long after him) that ultimately led to the calculus of Newton and Leibniz with many advances along the way to that.